Title: Going to Extremes: A parametric study on PeakOverThreshold and other methods
1Going to Extremes A parametric study on
Peak-Over-Thresholdand other methods
- Wiebke Langreder
- Jørgen Højstrup
- Suzlon Energy A/S
2Nightmare... Extreme Winds...
Source Wind Power Monthly
3Contents
- Introduction
- Objective
- Methodology
- Results and Conclusions
4Importance of Extreme Wind
- The 50-year maximum 10-minute average wind speed
Vref is one of the important factors to classify
a site according to IEC 61400-1.
Source IEC 61400-1 ed 3
5General Problem
- Extreme winds are not related with mean wind
speed. - Example
6Where do we get the information from?
Source IEC 61400-1 ed 2
7Where do we get the information from?
- EWTS (European Wind Turbine Standard)?
- connection between Weibull k factor and extreme
winds
Vave8m/s
decreasing k
8EWTS
Vref/Vave
Vref factor Vave
Weibull shape parameter k
Source EWTS
9Where do we get the information from?
- Gumbel Distribution?
- Extreme events in nature can frequently be
described by a Gumbel distribution - Measured maximum wind speeds are fitted to Gumbel
distribution - Gumbel distribution is extrapolated to 50-year
recurrence time
10The objective
- Ideal
- Long-term data available with several occurances
of - 50-year event
- Real world
- Only short term data available (1 year or more)
- Task
- How well can we estimate Vref?
- Compare different methods using short-term data
- IEC
- EWTS
- Gumbel
11Method
- Long-time series are split in shorter sub-sets,
each method is applied to each sub-set.
LT
We need a true reference value for comparison!
12True Reference Value
- Assumption
- The true Vref is determined applying
- Gumbel distribution
- FULL data set
- POT (Peak-over-Threshold)
13Method
- Results from all methods have been normalised
with this true value.
POT LT ? True Vref
N subsets ? N results per method ? Standard
deviation ? Bias
14Test Data
15The objective
- Compare different methods
- IEC
- Determine mean wind speed of each sub-set
- Multiply with factor 5
- Normalise result with true value
- EWTS
- Gumbel
16Findings - IEC
17Findings - IEC
- IEC is dependent on Weibull k factor
- Standard Deviation is 26!!!
- Average of all results fits the true value
bias 0
18The objective
- Compare different methods
- IEC
- EWTS
- Identify k factor of each sub-set
- Determine corresponding factor to multiply Vave
with - Normalise result with true value
- Gumbel
19EWTS
- EWTS does not specify
- Shall we use the 360 degree k factor?
- Shall we use a sector-specific k factor?
20Findings EWTS
- 360 degree
- Not dependent on k factor
- Negative bias of 9
- EWTS predicts less than our assumed true
reference value - Standard deviation is 16
- Sector
- Not dependent on k factor
- Positive bias of 7
- EWTS predicts more than our assumed true
reference value - Standard deviation is 16
21The objective
- Compare different methods
- IEC
- EWTS
- Gumbel
- How to identify maxima?
22Methods to identify maximum wind speeds
- Two commonly used methods
- POT Peak-over-Threshold (using WindPRO)
- PM Periodical Maximum
23POT Peak-over-Threshold
- Pick a threshold wind speed and identify all wind
speeds above - Introduce independency criteria
- Two options
- wind speed
- dynamic pressure (square of wind speed)
- Every result has been normalised with the
reference value. - The average of all results and their standard
deviation has been calculated.
24Ideal Gumbel Plot
25POT-Problems start...several slopes
26POT Influence of threshold
Two sub-sets from one site
27Findings Gumbel - POT
- deviations from the Gumbel distribution lead to
dependency of result from threshold - strong variations between individual sub-sets
- inconclusive regarding how threshold influences
result
- POT Wind
- Positive bias of 4
- Standard deviation is 12.
- POT Dynamic Pressure
- Negative bias of 4
- Standard deviation is 11
28Methods to identify maximum wind speeds
- Two commonly used methods
- POT Peak-over-Threshold
- PM Periodical Maximum
- Cut data set in sub-sections
- Identify maximum wind speed in each sub-section
- Ensure statistic independence between samples
29Findings Gumbel - PM
30Findings Gumbel - PM
31Findings Gumbel - PM
- Seasonal bias problematic but can be avoided
choosing periods carefully - Smallest recommended period is 6 months
- Method cannot be applied to the same sub-sets as
the other methods because of seasonal bias - Thus statistics cannot be compared with the other
results
32Summary Findings
/- 1 std dev
33Summary Findings
34Brute Force?
When added
35Conclusion
- IEC (factor 5) is not working
- PM not suitable for short-term data sets (lt5
years) - Always standard deviation gt10
- Squared wind speed (dynamic pressure) results in
lower Vref than wind data - Combination of methods possible, leading to a
small bias and standard deviation comparable to
Gumbel
36Acknowledgement
- We would like to thank www.winddata.com for
providing data.